Purpose
These exercises and activities are for students to use independently of the teacher to practice number properties.
Specific Learning Outcomes
- Divide items into equal pieces
- Share by dealing pieces
- Use the symbols for the mixed numbers and improper fractions
Description of Mathematics
Proportions and Ratios, EA (Stage 5)
Required Resource Materials
- Practice exercises with answers (PDF or Word)
- Homework with answers (PDF or Word)
Activity
Prior knowledge
- The activity ‘fraction circles’ (Book 7, pages 9 and 10) as well as fair shares (Book 7, pages 2 to 4) should have already been taught
- Identify that in a fraction, all the pieces are the same size
- Recognise symbols for 1/2, 1/4 etc
- The link between the number of equal pieces an item is cut into, and the name of the fraction
Background
There are a several significant ideas that arise in this activity, and need to be addressed in the teaching that precedes these activities.
- It cannot be assumed that students have the skill to accurately divide a shape into equal pieces – if there are no marks or guides to work from. In the process of halving, students pass through a developmental process. A child’s understanding of one half develops through as number of stages before it can be represented precisely. As a continuous quantity, involving tasks like cutting lengths of string, these stages are:
- One half as a multiple sequence of subdivisions, (where preschoolers simply do not know when to stop cutting…);
- One half as a single subdivision where there is gross inequality in each part (the whole is simply cut into 2 parts);
- One half as a single subdivision with remainder (here some attention to equality is made with the first cut, then ‘a remainder’ is usually cut off the large piece and discarded;
- One half as a single subdivision into 2 equal parts that uses all of the material (here eye movements and/or a finger movements are used to check the relative size of the pieces before cutting, and the size of the pieces is checked after cutting).
Cutting into 4, 3 and 5 pieces all require different strategies for success
- The concept of the fraction as 5 items each cut into 2 pieces is being created here. This can lead to a confusion between proper fractions and mixed numbers (3/4 and 3 3/4) as the numerator is seen as the 3 wholes…
Working with cutting shapes and dividing written lines should be included with the written problems.
Comments on the Exercises
Exercise 1
Asks students to draw pictures to help solve problems that involve a number of people sharing equally a set of items. For example, 4 people share 3 bags of popcorn between them. How much of a bag will each person get. In this questions there are more people than items so the answers are less than 1.
Exercise 2
Asks students to draw pictures to help solve problems that involve a number of people sharing equally a set of items. But in these questions the answers are greater than 1.